All results for two phase flow problems are compared to the solution of the Riemann problem obtained with the Newton method using the tolerance \(\varepsilon _{tol} = 10^{-9}\) .
More precisely, since in some cases the standard Newton method failed to converge, we used the Newton-Armijo method as presented in Kelley [1]}.
The saturation pressure is calculated using the steam tables Ref. [2]}.
If not stated otherwise we used the exact solution of the Riemann problem at the phase boundary in our numerical calculations as Riemann solvers. In the two phase flow examples away from the phase boundary any Riemann solver can be used. Here we applied for the numerical solution of the two phase flow examples the HLL solver as presented in Toro[3]}. In our first test, where the full compressible Euler equations are solved, we use an exact Riemann solver.
